## How to recover all the space of my main partition?

How to delete a container disk and reclaim space with the primary partition?

and after following the answer step, I lost the second partition and I only have one partition with 60 GB of my 120 GB

How to reclaim space?

## topological dynamics – A reference to the fact that a topologically transitive action of a group on a compact metric space has a dense orbit

I need an appropriate reference to the following obvious fact:

A group action $$G$$ on a compact metrable space $$K$$ is topologically transitive (= the orbit of any non-empty open set is dense) if and only if it is the orbit $$Gx$$ from a certain point $$x in K$$ is dense in $$K$$.

For a cyclic group, this characterization is proven here. I hope that some textbooks on topological dynamics should contain such a basic fact. Help me!

## labeling – V12.1 shows extra space using BarChart3D compared to V12

V 12.1 on Windows 10 shows additional space above and below `BarChart3D` compared to V 12 using the same code.

I would like to put a label on top of it below, but the space always where the bars stop and the label is too large with V 12.1. This does not happen in V12. All on the same PC.

I have tried different ways to put the label, and the empty space still does not shrink. i tried `Labeled` also and `Grid`. Also tried to add `ImageMargins -> 0, ImagePadding -> 0` optional at `BarChart3D` but this had no effect on reducing the white space above and below.

Here's the one I'm using now.

``````dataForChart = {{0.8, 0, 0, 99.2}, {14.285, 0, 0, 100},
{28.571, 0, 14.285, 57.1428}, {0, 0, 0, 100}, {28.571,0, 14.2857, 57.142857},
{28.5714,0, 0, 71.42857}, {57.14285, 0, 14.28571, 28.57142}};

casNames = {
Text@Style("Rubi", Bold, 10),
Text@Style("Mathematica", Bold, 10),
Text@Style("Maple", Bold, 10),
Text@Style("FriCAS", Bold, 10),
Text@Style("Giac/Xcas", Bold, 10),
Text@Style("Sympy", Bold, 10),
Text@Style("Maxima", Bold, 10)
};

percentageSolvedByRubi = 99.2;
percentageSolvedByM = 85.714;
percentageSolvedByMaple = 71.4286;
percentageSolvedByFricas = 100.;
percentageSolvedByGiac = 71.4286;
percentageSolvedBySympy = 71.4286;
percentageSolvedByMaxima = 42.8571;

Grid(
{
{Text(Style("Antiderivative Grade distribution for each CAS", 20))},
{Text(Style(
"Numbers shown on bars are total percentage solved for each CAS",
10))},
{
BarChart3D(
dataForChart,
ChartLayout -> "Percentile",
ChartStyle -> { Red,
RGBColor(255/255, 255/255, 0/255),
RGBColor(51/255, 51/255, 255/255),
RGBColor(50/255, 205/255, 50/255)},
ChartLabels -> {Placed(casNames, Below ), None},
ImageSize -> 500,
FaceGrids -> None,
Axes -> False,
ChartBaseStyle -> EdgeForm(None),
ImageSize -> 400,
PlotRange -> {0, 110},
BarSpacing -> 1.4, PlotTheme -> "Classic", Background -> None,
Lighting -> None, Method -> {"Canvas" -> None},
ChartLegends -> {"F", "C", "B", "A"},
Epilog -> {(*same order as names listed above*)
Text(
Style(ToString(Round(percentageSolvedByRubi, 0.01)) <> "%",
Bold), Scaled({.14, .6})),
Text(
Style(ToString(Round(percentageSolvedByM, 0.01)) <> "%", Bold),
Scaled({.25, .6})),
Text(
Style(ToString(Round(percentageSolvedByMaple, 0.01)) <> "%",
Bold), Scaled({.37, .6})),
Text(
Style(ToString(Round(percentageSolvedByFricas, 0.01)) <> "%",
Bold), Scaled({.48, .6})),
Text(
Style(ToString(Round(percentageSolvedByGiac, 0.01)) <> "%",
Bold), Scaled({.61, .6})),
Text(
Style(ToString(Round(percentageSolvedBySympy, 0.01)) <> "%",
Bold), Scaled({.72, .6})),
Text(
Style(ToString(Round(percentageSolvedByMaxima, 0.01)) <> "%",
Bold), Scaled({.84, .6}))
}
)
}
}, Frame -> All, Spacings -> {1, 0})
``````

Performing the above gives

Any suggestion as to what to do?

Thanks to Kglr's comments, I tried this on the cloud. The space is indeed gone, but the numbers on the bar graphs are now offset from their appearance in the notepad. It’s way too strange.

Update:

I just found out that it could be a bug! I tried the same code on V 12 on the same PC, and this is the output

Is this a bug ??

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## How to free up space in Google Storage

My Google storage has recently filled up, mainly due to Google Photos. I deleted some things from the player and released a few GB, which was mysteriously used again in about a week. Since then, I delete photos (deletion includes emptying the trash). The problem is that it didn't seem to free up any space. Curious, I checked one.google.com/storage, deleted some photos, and checked again. Nothing has changed. I thought it might be taking a while so I waited. About a week and 2000 photos deleted later, there was a negligible change (the space actually used increases 10 MB). And to reiterate, I also deleted all the files from the trash. I have no idea what's going on. Anyone have any idea what's going on?

## algorithms – Algorithmic problem with many different solutions of time / space complexity

I am preparing a lesson on algorithmic thinking for novice programmers. I would like to show them an easy to understand problem that has as many solutions as possible with different temporal or spatial complexities. Sorting comes to mind quickly, but if you avoid intentionally stupid solutions like Bogosort, you really only have the complexities O (n ^ 2) and O (n * log n).

In this regard, I like the problem of calculating the nth Fibonacci number with whole arithmetic. You can do it exponentially as a naive approach, linearly if you are a little smart, and even logarithmically if you are smart like hell. On the other hand, fibonacci numbers would not seem very practical to novice programmers. I would like something related to more practical issues because I don't want students to think that designing algorithms is something really abstract and theoretical.

## python – Format sub-traces with Matplotlib – Legend, titles, space

I am trying to use subplots with my data but the result is ugly. Could you improve my code? For a reproducible example, I provide data.

``````plot_data1.to_json()
'{"('price', 'cu2003')":{"0.0":0.0,"0.05":0.0,"0.1":0.0,"0.15000000000000002":0.0,"0.2":0.0,"0.25":0.0108436348,"0.30000000000000004":0.0216146115,"0.35000000000000003":0.0216755175,"0.4":0.0218316778,"0.45":0.0219418541,"0.5":0.0220531481,"0.55":0.0325273772,"0.6000000000000001":0.0433041031,"0.65":0.0437588885,"0.7000000000000001":0.0441111601,"0.75":0.0561041293,"0.8":0.0657966882,"0.8500000000000001":0.08670207,"0.9":0.110314396,"0.9500000000000001":0.1924818841,"1.0":0.5920403465},"('price', 'cu2004')":{"0.0":0.0,"0.05":0.0,"0.1":0.0,"0.15000000000000002":0.0,"0.2":0.0,"0.25":0.0215354797,"0.30000000000000004":0.02159594,"0.35000000000000003":0.0217367677,"0.4":0.0218221495,"0.45":0.0219514872,"0.5":0.02236386,"0.55":0.0431825542,"0.6000000000000001":0.0435492651,"0.65":0.0438260107,"0.7000000000000001":0.0449387709,"0.75":0.065267051,"0.8":0.0666592601,"0.8500000000000001":0.0876136239,"0.9":0.1118193,"0.9500000000000001":0.1999777802,"1.0":0.7091412742},"('price', 'cu2005')":{"0.0":0.0,"0.05":0.0,"0.1":0.0,"0.15000000000000002":0.0,"0.2":0.0107388316,"0.25":0.0214569252,"0.30000000000000004":0.0215354797,"0.35000000000000003":0.0216896215,"0.4":0.0217841194,"0.45":0.0219178082,"0.5":0.0323275862,"0.55":0.0430338892,"0.6000000000000001":0.0434074878,"0.65":0.0437301848,"0.7000000000000001":0.0537172325,"0.75":0.0649420933,"0.8":0.0664378253,"0.8500000000000001":0.0871934605,"0.9":0.1107787748,"0.9500000000000001":0.1994901917,"1.0":0.7296849088},"('price', 'cu2006')":{"0.0":0.0,"0.05":0.0,"0.1":0.0,"0.15000000000000002":0.0,"0.2":0.0107596299,"0.25":0.0109075044,"0.30000000000000004":0.0214615302,"0.35000000000000003":0.0215308429,"0.4":0.0217556837,"0.45":0.0221116639,"0.5":0.0324815938,"0.55":0.0332299513,"0.6000000000000001":0.0430848772,"0.65":0.0437015186,"0.7000000000000001":0.0541653125,"0.75":0.0645647261,"0.8":0.066830029,"0.8500000000000001":0.0870890486,"0.9":0.111049417,"0.9500000000000001":0.1952701237,"1.0":0.739677633},"('price', 'cu2007')":{"0.0":0.0,"0.05":0.0,"0.1":0.0,"0.15000000000000002":0.0,"0.2":0.0107307651,"0.25":0.0108342362,"0.30000000000000004":0.0109349371,"0.35000000000000003":0.0214661372,"0.4":0.0216731686,"0.45":0.0220361393,"0.5":0.0322026621,"0.55":0.0326299761,"0.6000000000000001":0.0427853246,"0.65":0.0435019032,"0.7000000000000001":0.0536768653,"0.75":0.0554877372,"0.8":0.0665705093,"0.8500000000000001":0.0859660434,"0.9":0.1104362231,"0.9500000000000001":0.1879699248,"1.0":0.782196761},"('price', 'cu2008')":{"0.0":0.0,"0.05":0.0,"0.1":0.0,"0.15000000000000002":0.0106963312,"0.2":0.0108084738,"0.25":0.0109926349,"0.30000000000000004":0.0214178625,"0.35000000000000003":0.0216379963,"0.4":0.0221018897,"0.45":0.0321750322,"0.5":0.0326299761,"0.55":0.0428311382,"0.6000000000000001":0.0434877147,"0.65":0.0535274596,"0.7000000000000001":0.0545077946,"0.75":0.0649561546,"0.8":0.0759960916,"0.8500000000000001":0.0961846746,"0.9":0.1218431546,"0.9500000000000001":0.1988730527,"1.0":0.94578247},"('price', 'cu2009')":{"0.0":0.0,"0.05":0.0,"0.1":0.0,"0.15000000000000002":0.0,"0.2":0.010686044,"0.25":0.0107642626,"0.30000000000000004":0.0108283703,"0.35000000000000003":0.0212765957,"0.4":0.0215053763,"0.45":0.0216943269,"0.5":0.0320307495,"0.55":0.032449973,"0.6000000000000001":0.042593973,"0.65":0.0433228636,"0.7000000000000001":0.053561864,"0.75":0.0641162642,"0.8":0.074906367,"0.8500000000000001":0.0883782589,"0.9":0.1300672014,"0.9500000000000001":0.2331261101,"1.0":0.778679535},"('price', 'cu2010')":{"0.0":0.0,"0.05":0.0,"0.1":0.0,"0.15000000000000002":0.0106598444,"0.2":0.0107712193,"0.25":0.0110217128,"0.30000000000000004":0.0215354797,"0.35000000000000003":0.0319216855,"0.4":0.0323939099,"0.45":0.0427441761,"0.5":0.0532141337,"0.55":0.054206418,"0.6000000000000001":0.0646342777,"0.65":0.0747224594,"0.7000000000000001":0.0853697578,"0.75":0.0967014075,"0.8":0.1099989,"0.8500000000000001":0.1320422535,"0.9":0.1623025319,"0.9500000000000001":0.2554278416,"1.0":2.5132705016},"('price', 'cu2011')":{"0.0":0.0,"0.05":0.0,"0.1":0.0,"0.15000000000000002":0.0106462259,"0.2":0.0107921433,"0.25":0.0212811236,"0.30000000000000004":0.0216614318,"0.35000000000000003":0.0323415265,"0.4":0.0431872166,"0.45":0.0539548937,"0.5":0.0650406504,"0.55":0.0758972135,"0.6000000000000001":0.0873362445,"0.65":0.0985761227,"0.7000000000000001":0.1099021871,"0.75":0.1275645796,"0.8":0.1402827236,"0.8500000000000001":0.1620045361,"0.9":0.2016129032,"0.9500000000000001":0.3650442478,"1.0":2.5024587477},"('price', 'cu2012')":{"0.0":0.0,"0.05":0.0,"0.1":0.0,"0.15000000000000002":0.0106269926,"0.2":0.0107296137,"0.25":0.0109625082,"0.30000000000000004":0.0214546235,"0.35000000000000003":0.0318775901,"0.4":0.0324184137,"0.45":0.0429000429,"0.5":0.0532028091,"0.55":0.0638365784,"0.6000000000000001":0.0744522442,"0.65":0.085515767,"0.7000000000000001":0.0965043963,"0.75":0.1092060719,"0.8":0.1280956447,"0.8500000000000001":0.1486357363,"0.9":0.1768542058,"0.9500000000000001":0.2403846154,"1.0":1.3820441397},"('price', 'cu2101')":{"0.0":0.0,"0.05":0.0,"0.1":0.0,"0.15000000000000002":0.0106168383,"0.2":0.0107933081,"0.25":0.0214247456,"0.30000000000000004":0.031870817,"0.35000000000000003":0.04264847,"0.4":0.0531067446,"0.45":0.0638841567,"0.5":0.0750509274,"0.55":0.0860770389,"0.6000000000000001":0.0967950097,"0.65":0.1076310408,"0.7000000000000001":0.1183686646,"0.75":0.1379749522,"0.8":0.1543380002,"0.8500000000000001":0.1828153565,"0.9":0.2363304329,"0.9500000000000001":0.7269617276,"1.0":2.8963414634},"('price', 'cu2102')":{"0.0":0.0,"0.05":0.0,"0.1":0.0,"0.15000000000000002":0.0,"0.2":0.0106871861,"0.25":0.0212134069,"0.30000000000000004":0.0322130355,"0.35000000000000003":0.0537345513,"0.4":0.0873553178,"0.45":0.1270244522,"0.5":0.1591005515,"0.55":0.1960143744,"0.6000000000000001":0.2392604676,"0.65":0.2866546342,"0.7000000000000001":0.32873807,"0.75":0.3646894776,"0.8":0.4151586119,"0.8500000000000001":0.4710416444,"0.9":0.5397819281,"0.9500000000000001":0.7334963325,"1.0":3.0713447798}}'
plot_data2 = df_min_chng_3m.quantile(np.arange(0,1.05, 0.05)) *100
'{"('price', 'cu2003')":{"0.0":0.0,"0.05":0.0,"0.1":0.0,"0.15000000000000002":0.0,"0.2":0.0,"0.25":0.0108436348,"0.30000000000000004":0.0216146115,"0.35000000000000003":0.0216755175,"0.4":0.0218316778,"0.45":0.0219418541,"0.5":0.0220531481,"0.55":0.0325273772,"0.6000000000000001":0.0433041031,"0.65":0.0437588885,"0.7000000000000001":0.0441111601,"0.75":0.0561041293,"0.8":0.0657966882,"0.8500000000000001":0.08670207,"0.9":0.110314396,"0.9500000000000001":0.1924818841,"1.0":0.5920403465},"('price', 'cu2004')":{"0.0":0.0,"0.05":0.0,"0.1":0.0,"0.15000000000000002":0.0,"0.2":0.0,"0.25":0.0215354797,"0.30000000000000004":0.02159594,"0.35000000000000003":0.0217367677,"0.4":0.0218221495,"0.45":0.0219514872,"0.5":0.02236386,"0.55":0.0431825542,"0.6000000000000001":0.0435492651,"0.65":0.0438260107,"0.7000000000000001":0.0449387709,"0.75":0.065267051,"0.8":0.0666592601,"0.8500000000000001":0.0876136239,"0.9":0.1118193,"0.9500000000000001":0.1999777802,"1.0":0.7091412742},"('price', 'cu2005')":{"0.0":0.0,"0.05":0.0,"0.1":0.0,"0.15000000000000002":0.0,"0.2":0.0107388316,"0.25":0.0214569252,"0.30000000000000004":0.0215354797,"0.35000000000000003":0.0216896215,"0.4":0.0217841194,"0.45":0.0219178082,"0.5":0.0323275862,"0.55":0.0430338892,"0.6000000000000001":0.0434074878,"0.65":0.0437301848,"0.7000000000000001":0.0537172325,"0.75":0.0649420933,"0.8":0.0664378253,"0.8500000000000001":0.0871934605,"0.9":0.1107787748,"0.9500000000000001":0.1994901917,"1.0":0.7296849088},"('price', 'cu2006')":{"0.0":0.0,"0.05":0.0,"0.1":0.0,"0.15000000000000002":0.0,"0.2":0.0107596299,"0.25":0.0109075044,"0.30000000000000004":0.0214615302,"0.35000000000000003":0.0215308429,"0.4":0.0217556837,"0.45":0.0221116639,"0.5":0.0324815938,"0.55":0.0332299513,"0.6000000000000001":0.0430848772,"0.65":0.0437015186,"0.7000000000000001":0.0541653125,"0.75":0.0645647261,"0.8":0.066830029,"0.8500000000000001":0.0870890486,"0.9":0.111049417,"0.9500000000000001":0.1952701237,"1.0":0.739677633},"('price', 'cu2007')":{"0.0":0.0,"0.05":0.0,"0.1":0.0,"0.15000000000000002":0.0,"0.2":0.0107307651,"0.25":0.0108342362,"0.30000000000000004":0.0109349371,"0.35000000000000003":0.0214661372,"0.4":0.0216731686,"0.45":0.0220361393,"0.5":0.0322026621,"0.55":0.0326299761,"0.6000000000000001":0.0427853246,"0.65":0.0435019032,"0.7000000000000001":0.0536768653,"0.75":0.0554877372,"0.8":0.0665705093,"0.8500000000000001":0.0859660434,"0.9":0.1104362231,"0.9500000000000001":0.1879699248,"1.0":0.782196761},"('price', 'cu2008')":{"0.0":0.0,"0.05":0.0,"0.1":0.0,"0.15000000000000002":0.0106963312,"0.2":0.0108084738,"0.25":0.0109926349,"0.30000000000000004":0.0214178625,"0.35000000000000003":0.0216379963,"0.4":0.0221018897,"0.45":0.0321750322,"0.5":0.0326299761,"0.55":0.0428311382,"0.6000000000000001":0.0434877147,"0.65":0.0535274596,"0.7000000000000001":0.0545077946,"0.75":0.0649561546,"0.8":0.0759960916,"0.8500000000000001":0.0961846746,"0.9":0.1218431546,"0.9500000000000001":0.1988730527,"1.0":0.94578247},"('price', 'cu2009')":{"0.0":0.0,"0.05":0.0,"0.1":0.0,"0.15000000000000002":0.0,"0.2":0.010686044,"0.25":0.0107642626,"0.30000000000000004":0.0108283703,"0.35000000000000003":0.0212765957,"0.4":0.0215053763,"0.45":0.0216943269,"0.5":0.0320307495,"0.55":0.032449973,"0.6000000000000001":0.042593973,"0.65":0.0433228636,"0.7000000000000001":0.053561864,"0.75":0.0641162642,"0.8":0.074906367,"0.8500000000000001":0.0883782589,"0.9":0.1300672014,"0.9500000000000001":0.2331261101,"1.0":0.778679535},"('price', 'cu2010')":{"0.0":0.0,"0.05":0.0,"0.1":0.0,"0.15000000000000002":0.0106598444,"0.2":0.0107712193,"0.25":0.0110217128,"0.30000000000000004":0.0215354797,"0.35000000000000003":0.0319216855,"0.4":0.0323939099,"0.45":0.0427441761,"0.5":0.0532141337,"0.55":0.054206418,"0.6000000000000001":0.0646342777,"0.65":0.0747224594,"0.7000000000000001":0.0853697578,"0.75":0.0967014075,"0.8":0.1099989,"0.8500000000000001":0.1320422535,"0.9":0.1623025319,"0.9500000000000001":0.2554278416,"1.0":2.5132705016},"('price', 'cu2011')":{"0.0":0.0,"0.05":0.0,"0.1":0.0,"0.15000000000000002":0.0106462259,"0.2":0.0107921433,"0.25":0.0212811236,"0.30000000000000004":0.0216614318,"0.35000000000000003":0.0323415265,"0.4":0.0431872166,"0.45":0.0539548937,"0.5":0.0650406504,"0.55":0.0758972135,"0.6000000000000001":0.0873362445,"0.65":0.0985761227,"0.7000000000000001":0.1099021871,"0.75":0.1275645796,"0.8":0.1402827236,"0.8500000000000001":0.1620045361,"0.9":0.2016129032,"0.9500000000000001":0.3650442478,"1.0":2.5024587477},"('price', 'cu2012')":{"0.0":0.0,"0.05":0.0,"0.1":0.0,"0.15000000000000002":0.0106269926,"0.2":0.0107296137,"0.25":0.0109625082,"0.30000000000000004":0.0214546235,"0.35000000000000003":0.0318775901,"0.4":0.0324184137,"0.45":0.0429000429,"0.5":0.0532028091,"0.55":0.0638365784,"0.6000000000000001":0.0744522442,"0.65":0.085515767,"0.7000000000000001":0.0965043963,"0.75":0.1092060719,"0.8":0.1280956447,"0.8500000000000001":0.1486357363,"0.9":0.1768542058,"0.9500000000000001":0.2403846154,"1.0":1.3820441397},"('price', 'cu2101')":{"0.0":0.0,"0.05":0.0,"0.1":0.0,"0.15000000000000002":0.0106168383,"0.2":0.0107933081,"0.25":0.0214247456,"0.30000000000000004":0.031870817,"0.35000000000000003":0.04264847,"0.4":0.0531067446,"0.45":0.0638841567,"0.5":0.0750509274,"0.55":0.0860770389,"0.6000000000000001":0.0967950097,"0.65":0.1076310408,"0.7000000000000001":0.1183686646,"0.75":0.1379749522,"0.8":0.1543380002,"0.8500000000000001":0.1828153565,"0.9":0.2363304329,"0.9500000000000001":0.7269617276,"1.0":2.8963414634},"('price', 'cu2102')":{"0.0":0.0,"0.05":0.0,"0.1":0.0,"0.15000000000000002":0.0,"0.2":0.0106871861,"0.25":0.0212134069,"0.30000000000000004":0.0322130355,"0.35000000000000003":0.0537345513,"0.4":0.0873553178,"0.45":0.1270244522,"0.5":0.1591005515,"0.55":0.1960143744,"0.6000000000000001":0.2392604676,"0.65":0.2866546342,"0.7000000000000001":0.32873807,"0.75":0.3646894776,"0.8":0.4151586119,"0.8500000000000001":0.4710416444,"0.9":0.5397819281,"0.9500000000000001":0.7334963325,"1.0":3.0713447798}}'

f, ax = plt.subplots(2,1)

colors = ('#a6cee3','#1f78b4','#b2df8a','#33a02c','#fb9a99','#e31a1c','#fdbf6f',
'#ff7f00','#cab2d6','#6a3d9a','#ffff99','#b15928')
plot_data1.plot(kind = 'bar', color = colors, ax = ax(0))
plt.title('Quantiles of Maximum Percent Change of Price over a 3 Minutes window', fontsize = 18)

plt.ylabel('Maximum Percent Change of Price n Over a 3 minutes window (%)')
xs = plt.xticks()
plt.xticks(xs(0), (f'{x:.2f}' for x in plot_data.index))

colors = ('#a6cee3','#1f78b4','#b2df8a','#33a02c','#fb9a99','#e31a1c','#fdbf6f',
'#ff7f00','#cab2d6','#6a3d9a','#ffff99','#b15928')
plot_data2.plot(kind = 'bar', color = colors, ax = ax(1))
plt.title('Quantiles of Minimum Percent Change of Price over a 3 Minutes window', fontsize = 18)

plt.ylabel('Minimum Percent Change of Price n Over a 3 minutes window (%)')
xs = plt.xticks()
plt.xticks(xs(0), (f'{x:.2f}' for x in plot_data.index))
``````

## does the struct * s1 node in the main function allocate 4 bytes of memory space?

Structure node
{int data;
Next structure node *;
};

void main ()
{struct node * s1; / * does this declaration allocate 4 bytes of memory space to the pointer s1? * /
}

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